On generating new solutions of the Ernst equation from old solutions
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Kyriakopoulos, E
(EN)
If E is an arbitrary generic solution of the Ernst equation and E its complex conjugate the most general expression E'=G(E, E, rho , z), is determined which is also a solution of this equation. If E is complex it is shown that G cannot depend on E and E simultaneously, and that the most general E' is the Ehlers transformation. Also it is proven that, if E is real, the most general E' is E'=(Ec+ic1ew)/(ic2E c+ew), where c, c1 and c2 are arbitrary real constants and w is an arbitrary real solution of the Laplace equation in the axially symmetric case. In addition two other expressions are given for E'. The three expressions can also be derived from the Ehlers transformation.
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